localstorage not being deleted

I have cookie set to delete everything, and all cookies are being deleted (except favorites) -- but when I check in Chrome or Safari website localstorage items remain and can only be deleted through the browser's options. Any thoughts about this?

yes, they are still displayed after a browser restart. A good example is NYPost.com, for which Safari and Chrome continue to indicate a local storage entry even after a browser restart and a system restart. I'm using MacOS 10.15.4 and updated browsers -- and the Mac App Store version of Cookie.

It seems that this does work as expected (i.e., localstorage databases are deleted) if the simple cookie user interface is selected, but localstorage databases are not deleted if the advanced interface is selected (no matter what deletion options are selected).

Yes, I'm sure these are not databases that are being regenerated by Safari upon launch. First, the problem exists in Safari, Chrome and Edge. Second, the databases that are retained are for random sites I've visited that are not in my favorites or would be pre-fetched by any browser for any reason.